Why did Italy not build a coastal-defence fleet?

Would coastal-defence ships have made sense for Italy and its overseas holdings?

Not especially; Italy needed full battleships that could move around the peninsula and face French or Austro-Hungarian fleets on either coast.

Italian overseas holdings lay within reach of the main fleet, while Italy's geography required warships to sail around the peninsula to move between operating areas. Competition with both France and Austria-Hungary therefore rewarded battleships with speed, range, and full fleet capability. A slow ship tied to one coast would have sacrificed the flexibility Italy needed most.